Difference between revisions of "Abs"

Latest revision as of 00:17, 8 March 2016

Abs(x)

The absolute value of a number, or the magnitude of a complex number.

For a non-negative real number, Abs(x) returns «x».

For a negative real number, Abs(x) returns -«x».

For a complex number, a + bj, Abs(x) returns the magnitude, equal to [math]\displaystyle{ \sqrt{a^2+b^2} }[/math].

Complex numbers

A complex number can be written in standard (cartesian) form as [math]\displaystyle{ a + b j }[/math], or in polar form as [math]\displaystyle{ r e^{\theta j} }[/math]. Given a complex number, «x», Abs(x) gives r, the magnitude from the polar form. The [math]\displaystyle{ \theta }[/math] is given by either ComplexRadians (or ComplexDegrees).

Examples

Abs(0) → 0

Abs(-0.123) → 0.123

Abs(4.534) → 4.534

Abs(-INF) → INF

Abs(-4-3j) → 5

Abs(1j) → 1

@@ Line 2: / Line 2: @@
 [[category:Functions that operate on complex numbers]]
 [[Category:Doc Status C]] <!-- For Lumina use, do not change -->
+==Abs(x)==
 The absolute value of a number, or the magnitude of a complex number.
-For a non-negative real number, <code>[[Abs]](x)</code> returns x.
+For a non-negative real number, [[Abs]](x) returns «x».
-For a negative real number, <code>[[Abs]](x)</code> returns -x.
+For a negative real number, [[Abs]](x) returns -«x».
-For a [[Complex Numbers|complex number]], ''a + bj'', <code>[[Abs]](x)</code> returns the magnitude, equal to <ldcmath>\sqrt{a^2+b^2}</ldcmath>.
+For a [[Complex Numbers|complex number]], ''a + bj'', [[Abs]](x) returns the magnitude, equal to <math>\sqrt{a^2+b^2}</math>.
-= Complex numbers =
+== Complex numbers ==
-A complex number can be written in standard (cartesian) form as <math>a + b j</math>, or in polar form as <math>r e^{\theta j}</math>. Given a complex number, x, <code>[[Abs]](x)</code> gives ''r'', the magnitude from the polar form.  The <math>\theta</math> is given by either [[ComplexRadians]] (or [[ComplexDegrees]]).
+A complex number can be written in standard (cartesian) form as <math>a + b j</math>, or in polar form as <math>r e^{\theta j}</math>. Given a complex number, «x», [[Abs]](x) gives ''r'', the magnitude from the polar form.  The <math>\theta</math> is given by either [[ComplexRadians]] (or [[ComplexDegrees]]).
-= Examples =
+== Examples ==
-:<code>[[Abs]](0)</code> &rarr; 0
+:<code>Abs(0) &rarr; 0</code>
-:<code>[[Abs]](-0.123)</code> &rarr; 0.123
+:<code>Abs(-0.123) &rarr; 0.123</code>
-:<code>[[Abs]](4.534)</code> &rarr; 4.534
+:<code>Abs(4.534) &rarr; 4.534</code>
-:<code>[[Abs]](-[[INF]])</code> &rarr; [[INF]]
+:<code>Abs(-INF) &rarr; INF</code>
-:<code>[[Abs]](-4-3j)</code> &rarr; 5
+:<code>Abs(-4-3j) &rarr; 5</code>
-:<code>[[Abs]](1j)</code> &rarr; 1
+:<code>Abs(1j) &rarr; 1</code>
-= See Also =
+== See Also ==
 * [[Sign]](x)
 * [[Complex Numbers]]
-* [[ComplexRadians]], [[ComplexDegrees]], [[ImPart]], [[RealPart]]
+* [[ComplexRadians]]
+* [[ComplexDegrees]]
+* [[ImPart]]
+* [[RealPart]]